Question

Prove that: $((1+a)^{(1/n)}-1)n$ is decreasing

score 80 · Answer 1 · 2018-09-26 19:07:49

80

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Prove that: $((1+a)^{(1/n)}-1)n$ is decreasing

Published on 26 Sep 2018 - 19:07

score 89 · Answer 2 · 2018-09-26 22:14:57

89

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Do you know how to prove $2(1-\cos x))<x^{2}$

Published on 26 Sep 2018 - 22:14

score 232 · Answer 3 · 2026-03-25 06:08:31

232

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Solve this inequality with nested radicals (possibly by induction)

Published on 25 Mar 2026 - 6:08

score 51 · Answer 4 · 2018-09-27 13:34:05

51

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Solving $-1\le \frac{2}{x}$, I came up with 2 opposite solutions

Published on 27 Sep 2018 - 13:34

score 149 · Answer 5 · 2026-04-02 08:54:07

149

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Prove: $x^4 + y^4 + z^4 - 4(x^3 + y^3 + z^3) + 5(x^2 + y^2 + z^2) \leqslant 4 $

Published on 02 Apr 2026 - 8:54

score 47 · Answer 6 · 2018-09-27 16:57:21

47

Views

Find real $x$ that satisfies $\frac{1}{1+x}>\frac{x}{x-1}$

Published on 27 Sep 2018 - 16:57

score 74 · Answer 7 · 2018-09-27 17:01:26

Can we find the relationship between $I$, $J$ and $K$ if $f(x)\geq 0$ for $x\in I$, $f(x)>g(x)$ for $x\in J$, and $f^2(x)>g^2(x)$ for $x\in K$?

score 140 · Answer 8 · 2026-03-25 16:03:49

140

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If $a^2+b^2 \gt a+b$ and $a,b \gt 0$ Prove that $a^3+b^3 \gt a^2+b^2$

Published on 25 Mar 2026 - 16:03

score 614 · Answer 9 · 2026-03-25 19:07:21

614

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Prove that $\lfloor x\rfloor \geq y$ if, and only if, $x\geq\lceil y\rceil$

Published on 25 Mar 2026 - 19:07

score 157 · Answer 10 · 2026-03-25 01:40:05

157

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Prove: for all $x \in (0, 1], 2^x+2^{\frac{1}{x}} \leqslant 2^{x+\frac{1}{x}}$

Published on 25 Mar 2026 - 1:40

score 83 · Answer 11 · 2018-09-28 16:54:32

83

Views

Power of arithmetic mean

Published on 28 Sep 2018 - 16:54

score 60 · Answer 12 · 2018-09-28 17:17:17

60

Views

If $a>0$, then $\frac{n^{a+1}}{a+1} < \sum_{1}^{n} k^a < \frac{(n+1)^{a+1}}{a+1}$?

Published on 28 Sep 2018 - 17:17

score 51 · Answer 13 · 2018-09-28 17:30:08

51

Views

Sum of exponential inequality using MVT

Published on 28 Sep 2018 - 17:30

score 106 · Answer 14 · 2018-09-28 17:45:45

106

Views

Inequality for probability distribution

Published on 28 Sep 2018 - 17:45

score 381 · Answer 15 · 2018-09-28 20:40:23

381

Views

Solution for $\frac{3}{x-9} \gt \frac{2}{x+2}$

Published on 28 Sep 2018 - 20:40

List Question

Prove that: $((1+a)^{(1/n)}-1)n$ is decreasing

Do you know how to prove $2(1-\cos x))<x^{2}$

Solve this inequality with nested radicals (possibly by induction)

Solving $-1\le \frac{2}{x}$, I came up with 2 opposite solutions

Prove: $x^4 + y^4 + z^4 - 4(x^3 + y^3 + z^3) + 5(x^2 + y^2 + z^2) \leqslant 4 $

Find real $x$ that satisfies $\frac{1}{1+x}>\frac{x}{x-1}$

Can we find the relationship between $I$, $J$ and $K$ if $f(x)\geq 0$ for $x\in I$, $f(x)>g(x)$ for $x\in J$, and $f^2(x)>g^2(x)$ for $x\in K$?

If $a^2+b^2 \gt a+b$ and $a,b \gt 0$ Prove that $a^3+b^3 \gt a^2+b^2$

Prove that $\lfloor x\rfloor \geq y$ if, and only if, $x\geq\lceil y\rceil$

Prove: for all $x \in (0, 1], 2^x+2^{\frac{1}{x}} \leqslant 2^{x+\frac{1}{x}}$

Power of arithmetic mean

If $a>0$, then $\frac{n^{a+1}}{a+1} < \sum_{1}^{n} k^a < \frac{(n+1)^{a+1}}{a+1}$?

Sum of exponential inequality using MVT

Inequality for probability distribution

Solution for $\frac{3}{x-9} \gt \frac{2}{x+2}$

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